How long does the suspension of cultures last?

I have prepared my bacterial strains in a suspension (culture in broth) fresh - which was incubated for 24 hours at 37 degree celcius- for use to inoculate the testing products and some of it remained.

Can I still use them when incubated at 37 degree celcius for another 48 hours for another experiments ?? or they have already passed the exponential growth and better to use fresh culture?

It depends on the species, the medium used and a few other factors, but most of the common bacterial species and strains used in the lab will only be in exponential phase growth for about 16 hours at 37, at most I would have thought. You can test this for yourself, by plotting OD600 vs time.